Do I need to use multisite or something else?

I want to create sites with domain names like this:

http://www.domain1.com
http://www.domain2.com
staging.domain1.com
staging.domain2.com

I want everything running on the same server and I want to avoid as much duplication as possible, i.e. don’t want multiple copies of WordPress code, databases, etc if I can possibly avoid it.

I *thought* that multisite could support this but maybe I’m getting confused with the Network functionality, since networks seem to require a common domain.

What am I misunderstanding, or do I need to do this completely differently?

Thanks.